Thank you very much for the visual contexts, and the musical contexts. I don't think I would have had the patience to parse the structure of Godel's arguments to fully appreciate what he was expressing; and yet I am such a fan of his work. I have spent years trying to understand his theorems in addition to understanding his seemingly surprising position against the current Zeigeist.
Thanks for this. I am going to have to watch this several more times obviously. If I understood correctly, our current Zeitgeist has certainly headed even further into the direction that Kurt Godel is warning us against and it seems anyone arguing outside of empiricism are branded as intellectual heretics. It is refreshing to hear an intellectual giant arguing in favour for that vague something extra that is missing beyond mechanical thinking (insight, intuition)
This video is truly amazing. Wish i could hear more modern ones that indulge the philosophy of mathematics more elaborately. Want to see how we have changed our perspective of such abstract and intuitive field of reasoning throughout time.
@kano26 thanks for the interest. Gödel didn't see philosophy advancing much since Leibniz, hegel, Kant and Husserl. So if it hasn't advanced much since Gödel's time, that isn't much of a surprise. Mathematical logic does continue to have advances however..very profound ones...i just don't think we have been able to keep up with the philosophical implications of these discoveries...
@GaryGeckDotCom Not really. Mathematics stands on its own, and has no relations to philosophy other than having similarities to logic. Mathematics, like logics, is a formal system based on certain axioms/assumptions through which you can derive general or specific knowledge about the formal system that you have constructed. I don't think one can say that philosophy is the foundation, but rather that you can philosophize about anything, including math. Do you agree?
@astroboomboy The "foundation o mathematics" is a topic that humanity presently can only approach with philosophy. This field is called the "philosophy of mathematics". To say that mathematics stands on its own is to say "mathematics stands independent without any foundation" which is not ok with me...it may be OK with you if you see math as only an arbitrary game. Godel saw it as requiring a solid foundation and only philosophy can do that in his day and in the present as well.
@GaryGeckDotCom I often wish that Gödel was right, but I do not really see any evidence to the idea that mathematics is anything but systems that refer to themselves using the axioms set up within that system.
But I do see your point, and it would be very interesting if we could find a foundation for mathematics that is what Gödel envisioned. However, I think his ideas about the human mind and its abilities where a bit off, but very interesting.
@GaryGeckDotCom I cannot see the mind as anything but the matter it consists of, and the emergent patterns of neural networks that matter is defined as when it is in any state. However, this has not led to any results in explaining the mind yet, so I can only read more and never make up my mind as to what reality is before we have a better understanding and a more solid foundation.
Can you recommend a book that explains Gödels ideas in a non-technical manner, if you know of one?
@astroboomboy As far as a book goes. The standard is Logical Dilemmas because it was written by Dawson who really was an expert on Godel. It has both technical ideas and biographical ones but you will be able to read it all.
@GaryGeckDotCom But Rucker's book is more a survey of relevant topics. It covers Gödel's work but this is just one part of it. Dawson's book is on Gödel only.
@astroboomboy As far as Gödel and the mind goes that is the big question. We don't know the answer. It's useful to clarify the options we have. One option is that humans think in a way that is consistent and complete and and somehow gets around the incompleteness phenomena. Another possible explanation is that all knowledge is complete and inconsistent and that all knowledge is a giant contradiction when taken as a whole "God is the point where all opposites coincide" -Cusa
@astroboomboy One option that is logically valid but no preferable nor intuitive (at least to Gödel, myself and some others) is that the mind is no greater than a Turing machine, in which case impossible problems that humans can't, even solve in theory, make up the majority of the problems in the universe of thought and we can only solve (in theory) an infinitesimal of these...even with infinite time and infinite number of people thinking about these.
@GaryGeckDotCom The theories and critiques of Turing machines are very subtle and seems to me misunderstood. Like the ability of a Turing machine to conceptualize infinity, or make infinite conceptual strings, something we humans seem to be able to (although this is not well defined nor demonstrated). I think the theories are too subtle to actually say anything about the human mind, computers, and it seems to me that the mind can be universal and a turing machine.
@astroboomboy Turing machines have limitations. Because they enumerate, ALL real nums are out of reach. It can enumerate any given real num though (ex. pi).
Turing machines can make infinite strings...they just can't make all infinite strings. Diagonalization demonstrates this intuitively. I see it as very well defined in terms of combinatorics.
Whether the mind is only a universal Turing machine is an open question still so you can say it can be or it can possibly not be the case too.
@GaryGeckDotCom There are many who criticize the idea that the Turing machine makes it impossible to create AI, and that the human mind has to be more than a turing machine. You have probably read Minsky, but his critique seems to be rather plausible, that even though turing machines can't make infinite strings there are shortcuts, and our mind uses such shortcuts to do these things.
@astroboomboy I have not undertaken a study of minksy but if you can point me to one select paper by minsky i will read it and comment. I don't get your reference as a result, but by 'shortcuts' do you mean like how we humans (and machines also) never write the infinite 0s in front of a number like we really should? I'd rather comment on a specific paper.
@GaryGeckDotCom I think we have to be careful in taking Gödels theorems outside of mathematics and projecting them onto the real world. And it actually may be so that there are infinite ways of looking at the universe, and our minds are only capable of certain interpretations that are approximations of the things in themselves (as Kant would put it). And as Kant would also state, time and space are the conditions of our faculties, not something "real" and so reality will always evade us somewhat
@astroboomboy We also need to be careful to distinguish between what Godel called "subjective mathematics" and "objective mathematics". His big question was are they the same or different? You clearly mean objective science which IS a formal system based on axioms standing alone. I am talking about subjective mathematics which is assumed by Godel and me to be broader..it mean mathematics as human mathematicians carry it out. So which of these two is mathematics, the discipline?
A version of this vid w/out musical soundtrack is now linked to from the description above towards the top...or in the video itself as an annotation...or just go to my videos channel.
Wow Gary, that was very interesting indeed!
I love how you draw directly on source material and state your sources so clearly.
umbalaba 4 days ago
Thank you very much for the visual contexts, and the musical contexts. I don't think I would have had the patience to parse the structure of Godel's arguments to fully appreciate what he was expressing; and yet I am such a fan of his work. I have spent years trying to understand his theorems in addition to understanding his seemingly surprising position against the current Zeigeist.
docerex 1 week ago
Thanks for this. I am going to have to watch this several more times obviously. If I understood correctly, our current Zeitgeist has certainly headed even further into the direction that Kurt Godel is warning us against and it seems anyone arguing outside of empiricism are branded as intellectual heretics. It is refreshing to hear an intellectual giant arguing in favour for that vague something extra that is missing beyond mechanical thinking (insight, intuition)
docerex 1 week ago
This video is truly amazing. Wish i could hear more modern ones that indulge the philosophy of mathematics more elaborately. Want to see how we have changed our perspective of such abstract and intuitive field of reasoning throughout time.
If anybody know of some good ones plz send link.
kano26 3 weeks ago
@kano26 thanks for the interest. Gödel didn't see philosophy advancing much since Leibniz, hegel, Kant and Husserl. So if it hasn't advanced much since Gödel's time, that isn't much of a surprise. Mathematical logic does continue to have advances however..very profound ones...i just don't think we have been able to keep up with the philosophical implications of these discoveries...
GaryGeckDotCom 3 weeks ago
Comment removed
EyonDreams 1 month ago
Comment removed
EyonDreams 1 month ago
Looking at math in a philosophical light ... why?
IceTeaMania 2 months ago
@IceTeaMania Philosophy is the foundation of mathematics.
GaryGeckDotCom 2 months ago
@GaryGeckDotCom Not really. Mathematics stands on its own, and has no relations to philosophy other than having similarities to logic. Mathematics, like logics, is a formal system based on certain axioms/assumptions through which you can derive general or specific knowledge about the formal system that you have constructed. I don't think one can say that philosophy is the foundation, but rather that you can philosophize about anything, including math. Do you agree?
astroboomboy 1 month ago
@astroboomboy The "foundation o mathematics" is a topic that humanity presently can only approach with philosophy. This field is called the "philosophy of mathematics". To say that mathematics stands on its own is to say "mathematics stands independent without any foundation" which is not ok with me...it may be OK with you if you see math as only an arbitrary game. Godel saw it as requiring a solid foundation and only philosophy can do that in his day and in the present as well.
GaryGeckDotCom 1 month ago
@GaryGeckDotCom I often wish that Gödel was right, but I do not really see any evidence to the idea that mathematics is anything but systems that refer to themselves using the axioms set up within that system.
But I do see your point, and it would be very interesting if we could find a foundation for mathematics that is what Gödel envisioned. However, I think his ideas about the human mind and its abilities where a bit off, but very interesting.
astroboomboy 1 month ago
@GaryGeckDotCom I cannot see the mind as anything but the matter it consists of, and the emergent patterns of neural networks that matter is defined as when it is in any state. However, this has not led to any results in explaining the mind yet, so I can only read more and never make up my mind as to what reality is before we have a better understanding and a more solid foundation.
Can you recommend a book that explains Gödels ideas in a non-technical manner, if you know of one?
astroboomboy 1 month ago
@astroboomboy As far as a book goes. The standard is Logical Dilemmas because it was written by Dawson who really was an expert on Godel. It has both technical ideas and biographical ones but you will be able to read it all.
GaryGeckDotCom 1 month ago
@GaryGeckDotCom I also recommend Rudy Rucker's Infinity and the Mind to everyone.
GaryGeckDotCom 1 month ago
@GaryGeckDotCom But Rucker's book is more a survey of relevant topics. It covers Gödel's work but this is just one part of it. Dawson's book is on Gödel only.
GaryGeckDotCom 1 month ago
@astroboomboy As far as Gödel and the mind goes that is the big question. We don't know the answer. It's useful to clarify the options we have. One option is that humans think in a way that is consistent and complete and and somehow gets around the incompleteness phenomena. Another possible explanation is that all knowledge is complete and inconsistent and that all knowledge is a giant contradiction when taken as a whole "God is the point where all opposites coincide" -Cusa
GaryGeckDotCom 1 month ago
@astroboomboy One option that is logically valid but no preferable nor intuitive (at least to Gödel, myself and some others) is that the mind is no greater than a Turing machine, in which case impossible problems that humans can't, even solve in theory, make up the majority of the problems in the universe of thought and we can only solve (in theory) an infinitesimal of these...even with infinite time and infinite number of people thinking about these.
GaryGeckDotCom 1 month ago
@GaryGeckDotCom The theories and critiques of Turing machines are very subtle and seems to me misunderstood. Like the ability of a Turing machine to conceptualize infinity, or make infinite conceptual strings, something we humans seem to be able to (although this is not well defined nor demonstrated). I think the theories are too subtle to actually say anything about the human mind, computers, and it seems to me that the mind can be universal and a turing machine.
astroboomboy 1 month ago
@astroboomboy Turing machines have limitations. Because they enumerate, ALL real nums are out of reach. It can enumerate any given real num though (ex. pi).
Turing machines can make infinite strings...they just can't make all infinite strings. Diagonalization demonstrates this intuitively. I see it as very well defined in terms of combinatorics.
Whether the mind is only a universal Turing machine is an open question still so you can say it can be or it can possibly not be the case too.
GaryGeckDotCom 1 month ago
@GaryGeckDotCom There are many who criticize the idea that the Turing machine makes it impossible to create AI, and that the human mind has to be more than a turing machine. You have probably read Minsky, but his critique seems to be rather plausible, that even though turing machines can't make infinite strings there are shortcuts, and our mind uses such shortcuts to do these things.
astroboomboy 1 month ago
@astroboomboy I have not undertaken a study of minksy but if you can point me to one select paper by minsky i will read it and comment. I don't get your reference as a result, but by 'shortcuts' do you mean like how we humans (and machines also) never write the infinite 0s in front of a number like we really should? I'd rather comment on a specific paper.
GaryGeckDotCom 1 month ago
@GaryGeckDotCom I think we have to be careful in taking Gödels theorems outside of mathematics and projecting them onto the real world. And it actually may be so that there are infinite ways of looking at the universe, and our minds are only capable of certain interpretations that are approximations of the things in themselves (as Kant would put it). And as Kant would also state, time and space are the conditions of our faculties, not something "real" and so reality will always evade us somewhat
astroboomboy 1 month ago
@astroboomboy We also need to be careful to distinguish between what Godel called "subjective mathematics" and "objective mathematics". His big question was are they the same or different? You clearly mean objective science which IS a formal system based on axioms standing alone. I am talking about subjective mathematics which is assumed by Godel and me to be broader..it mean mathematics as human mathematicians carry it out. So which of these two is mathematics, the discipline?
GaryGeckDotCom 1 month ago
@GaryGeckDotCom oops i meant objective mathematicsa above, not "objective science"...
GaryGeckDotCom 1 month ago
Well, at least now we see why he decided to never ever give this lecture.
NoMoarOxygen 2 months ago
This has been flagged as spam show
Occupy Together!
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infiniteinfiniteinfi 4 months ago
Love the video. Love the music.
Lewclan 5 months ago
@Lewclan Hans Zimmer - Inception
MyArchangelmichael 5 months ago
I thought the music and the video were both great. Btw what is the music?
Nine9Hundred00 6 months ago
@7:30 You misspelled the word "distracting".
ja524309 6 months ago
A version of this vid w/out musical soundtrack is now linked to from the description above towards the top...or in the video itself as an annotation...or just go to my videos channel.
GaryGeckDotCom 6 months ago 2
Lose the music.
AuntMartha 6 months ago
@AuntMartha I'm uploading a version sans music as we speak...will post link here.
GaryGeckDotCom 6 months ago
The pompous music is a bit distracting. Otherwise... good stuff!
JSKaartinen 6 months ago
@JSKaartinen hmm i'll post a version w/out music then too
GaryGeckDotCom 6 months ago
"This is Gary Geck and I am druuuuunk."
volpotmakmak 6 months ago 7
@volpotmakmak hahaha
GaryGeckDotCom 6 months ago